具有粗糙初值的Landau-Lifshitz-Gilbert方程的整体解的存在性
Global existence of Landau-Lifshitz-Gilbert system with rough initial data
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摘要: 关注高维Landau-Lifshitz-Gilbert方程的整体解的存在性问题,证明了当初始值半范数Z_0_BMO(R^n)充分小时,Landau-Lifshitz-Gilbert方程柯西问题存在整体解: 通过球面投射的方法, 把Landau-Lifshitz-Gilbert方程转化为一个非线性Schr\"odinger方程,然后研究该方程的整体解的存在性,最后通过逆运算,得到原来方程的解的整体存在性.Abstract: The global solutions to Landau-Lifshitz-Gilbert equation in high dimensions are considered. The global well-posedness of the Cauchy problem of the Landau-Lifshitz-Gilbert equation in R^n for any initial data Z_0\in S^2 with small Z_0_BMO(R^n) is established. The method is based on priori estimates of a nonlinear Schr\"odinger equation obtained from the Landau-Lifshitz-Gilbert equation by the stereographic projection.
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